Results 1 to 5 of 5

Math Help - computing the slope of the secant line between points

  1. #1
    JDS
    JDS is offline
    Member
    Joined
    Oct 2012
    From
    South Carolina
    Posts
    83

    computing the slope of the secant line between points

    Hello everyone. I am really getting lost trying to figure out how to correctly figure this one out. Here is the problem:

    Compute the slope of the secant line between the points at (a) x = 1 and x = 2, (b) x = 2 and x = 3, (c) x = 1.5 and x = 2, and (d) x = 2 and x = 2.5, (e) x = 1.9 and x = 2, (f) x = 2 and x = 2.1, and (g) use parts (a) - (f) and other calculations as needed to estimate the slope of the tangent line at x = 2.....

    f(x) = ex

    To give some context here, I have been learning (In Calculus: Early Transcendental Functions) about Differentiation, and specifically tangent lines and velocity.

    Any help with this problem would be greatly appreciated.

    Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2010
    Posts
    984
    Thanks
    237

    Re: computing the slope of the secant line between points

    The point of the problem is that as the second point approaches x=2 (from both directions), the secant line approaches the tangent line.

    What is a secant line? You just take two points on the graph and draw a line through them. So in (a), for example, you calculate f(1) and f(2) which are your y-values, and then just calculate the slope as:

    \frac{y_2-y_1}{x_2-x_1}

    - Hollywood
    Follow Math Help Forum on Facebook and Google+

  3. #3
    JDS
    JDS is offline
    Member
    Joined
    Oct 2012
    From
    South Carolina
    Posts
    83

    Re: computing the slope of the secant line between points

    Thanks Hollywood, I understand it a lot better now, however I do not quite understand how I am supposed to calculate f(1) and f(2), for example in (a), because the problem has f(x) = ex , So what am I supposed to do with the "e" or have I missed something somewhere?

    From what I gathered, to find f(x) = ex , replace the x with 1,which gives us f(x) = e1 , so what now?

    Thanks in advance!!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Mar 2010
    Posts
    984
    Thanks
    237

    Re: computing the slope of the secant line between points

    The symbol e just represents a number e=2.71828.... You probably have the e^x function on your calculator.

    So e^1=e is just a number, and so is e^2, e^{1.5}, etc.

    So for part (a), for example, the slope is:

    \frac{y_2-y_1}{x_2-x_1}=\frac{e^2-e^1}{2-1}=e^2-e\approx{4.67}

    - Hollywood
    Follow Math Help Forum on Facebook and Google+

  5. #5
    JDS
    JDS is offline
    Member
    Joined
    Oct 2012
    From
    South Carolina
    Posts
    83

    Re: computing the slope of the secant line between points

    Got ya, thanks Hollywood!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Slope of a secant line
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 11th 2010, 04:43 AM
  2. Slope of a secant line
    Posted in the Calculus Forum
    Replies: 9
    Last Post: May 10th 2010, 10:08 PM
  3. Secant Line Slope and Tangent Line Slope
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 26th 2009, 05:40 PM
  4. slope of the secant line
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 8th 2007, 12:47 PM
  5. Slope of Secant Line
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: January 19th 2007, 06:38 PM

Search Tags


/mathhelpforum @mathhelpforum